Continua whose hyperspace and suspension are homeomorphic

✍ Scribed by Sam B. Nadler Jr.; J. Quinn

• Book ID: 103094110
• Publisher: Elsevier Science
• Year: 1978
• Weight: 958 KB
• Volume: 8
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(78)90043-0

✦ Synopsis

continuum. By the hypezspace of X we mean C(X) = {A : A is a: nonempty subcontinuum of X) with the HausdorfI metric. The suspension S(X) of X is the quotient space (X .x I-1, + l])/R, where X X'[ -1, + 1] is the Cartesian product of X and the closed interval [ -1, + l] and R is the equivalence relation given by: (x,, t,)R(xz, t2) if and (only if t1= t2= +l, t,-tz= -1, or x1=x2 and tr= t2, It is shown that the arc is the only finitedimensional continuum whose hyperspace and suspension are homeomorphic. -I *-Ah& Subj. Class.: Primary 54B20; Secondary 54F20 a -triadic Cech cohomology composant of the point p decomposable continuum dimension HausdorfI metric / segment in the sense of Kelley Whitney map * _ 1